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Studies in Nonlinear Dynamics & Econometrics

Edited by: Jeremy Piger

Language: English

First published: April 1, 1996

Publication Frequency: 5 issues per year

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About this journal

Objective
A peer-reviewed journal since 1996, Studies in Nonlinear Dynamics & Econometrics (SNDE) is at the forefront of statistical and theoretical approaches to economics. The journal studies ways in which econometrics and dynamical systems theory increase our understanding of economic and financial markets. The journal disseminates authors' algorithms, programs, and data sets, allowing other scholars to replicate empirical results. Authors include econometricians such as Clive Granger, James Hamilton, and Halbert White, and theorists Jess Benhabib, Alan Kirman, and Kazuo Nishimura.

Best Paper Award
Since 2015, the Society has awarded $500 each year to the best paper published in the Society’s journal: Studies in Nonlinear Dynamics and Econometrics.

The Best Paper in 2024 for Studies in Nonlinear Dynamics and Econometrics, has been awarded to Francisco Blasques, Vladimír Holý and Petra Tomanová for their paper: "Zero-Inflated Autoregressive Conditional Duration Model for Discrete Trade Durations with Excessive Zeros." Studies in Nonlinear Dynamics & Econometrics, vol. 28, no. 5, 2024, pp. 673-702.

The Best Paper in 2023 for Studies in Nonlinear Dynamics and Econometrics, has been awarded to Thomas Lux for his paper: "Approximate Bayesian Inference for Agent-Based Models in Economics: A Case Study." Studies in Nonlinear Dynamics & Econometrics, vol. 27, no. 4, 2023, pp. 423-447.

The Best Paper in 2022 for Studies in Nonlinear Dynamics and Econometrics, has been awarded to Szabolcs Blazsek, Alvaro Escribano and Adrian Licht. for their paper: "Multivariate Markov-switching score-driven models: an application to the global crude oil market" Studies in Nonlinear Dynamics & Econometrics, vol. 26, no. 3, 2022, pp. 313-335.

The Best Paper in 2021 for Studies in Nonlinear Dynamics and Econometrics, has been awarded to Eric Mark Aldrich and Howard Kung for their paper: “Computational Methods for Production-Based Asset Pricing Models with Recursive Utility”, published in Volume 25, Issue 1.

The Best Paper in 2020 for Studies in Nonlinear Dynamics and Econometrics, has been awarded to Gregor Bäurle, Daniel Kaufmann, Sylvia Kaufmann and Rodney Strachan for their paper: “Constrained interest rates and changing dynamics at the zero lower bound”, published in Volume 24, Issue 2.

The Best Paper in 2019 for Studies in Nonlinear Dynamics and Econometrics, has been awarded to Chang-Jin Kim and Yunmi Kim for their paper: “A unified framework jointly explaining business conditions, stock returns, volatility and “volatility feedback news” effects”, published in Volume 23, Issue 2.

The Best Paper in 2018 for Studies in Nonlinear Dynamics and Econometrics, has been awarded to Luiggi Donayre, Yunjong Eo and James Morley for their paper: “Improving likelihood-ratio-based confidence intervals for threshold parameters in finite samples”,published in Volume 22, Issue 1 (Feb 2018)

The Best Paper in 2017 for Studies in Nonlinear Dynamics and Econometrics has been awarded to Julien Chevallier and Stephane Goutte for their paper: “On the estimation of regime-switching Levy models”, published in Volume 21, Issue 1 (Feb 2017).

The Best Paper in 2016 for Studies in Nonlinear Dynamics and Econometrics has been awarded to Mark J. Jensen for his paper: “Robust estimation of nonstationary, fractionally integrated, autoregressive, stochastic volatility?”, published in Volume 20, Issue 4 (Sept. 2016).

The Best Paper in 2015 for Studies in Nonlinear Dynamics and Econometrics has been awarded to Markus Jochmann and Gary Koop for their paper: “Regime-switching cointegration?”, published in Volume 19, Issue 1 (Feb 2015).

Topics

Probability
Statistics
Macroeconomics
Finance
Forecasting
Econometrics

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Research articles

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Your Benefits

Your benefits:

Theoretical and applied studies that characterize and motivate nonlinear phenomena
State-of the-art research results that increase understanding of economic and financial markets
Novel tools that allow replication of empirical results
High quality peer-review
International and renowned editorial board

History

Content available since 1996 (Volume 1, Issue 1)

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Big Swings in the Data and Perceived Changes in the Risk Premia

July 22, 2025

Martin Sola, Fabio Spagnolo, Francisco Terfi

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Stock markets experience periods where stocks or market returns are consistently higher than their mean and other periods where the individual stocks and markets’ volatility fluctuates from high to low. Since these periods do not necessarily coincide, a related question is whether periods where individual stock markets are higher than their mean, usually identified as αs different from zero in the conditional regressions, disappear once the researcher accounts for changing states of the economy. In this spirit, we develop and estimate a state-dependent version of the CAPM pricing model that accounts for considerable swings in the data. We use U.S. financial data to assess the model’s validity and find support for a state-dependent version of the CAPM for the data under consideration. We show how important it is to consider changes in stock and market returns and changes in their variance-covariances, and that, when not accounting for changes in market conditions, may spuriously yield significant α values. We stress that to assess changes in the risk premium, we should not only focus on βs but also allow for changes in the market premium; otherwise, changes in risk premia may be over- or underestimated. In addition, the classification between investment opportunities may be mistaken for a single regime model, even when rolling regressions are used.
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Covariance Matrix Estimation in Time-Varying Factor Models

July 14, 2025

Jingming Yao, Jianhong Wu

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This paper considers the covariance matrix estimation in time-varying factor models. A so-called two-step method is proposed to estimate the covariance matrix, which is shown to be more accurate for high-dimensional data. Simulation results show that the proposed method has desired performance under finite samples, especially for the case with rapidly changing factor loadings. The empirical study shows that the minimum variance portfolio constructed by this method has desired performance in terms of both return and risk control.
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From Model Misspecification to Multidimensional Welfare: A Conversation with Professor Esfandiar Maasoumi

July 10, 2025

Fredj Jawadi

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In this interview, Fredj Jawadi speaks with Dr. Esfandiar Maasoumi about his academic journey and research contributions. Professor Maasoumi reflects on his early education in Iran, his studies at the London School of Economics, and the significant influence of Professor Denis Sargan on his academic development. The conversation covers a broad range of topics, including model misspecification, estimator properties, asymmetry, nonlinearity, inequality, poverty, and well-being. Professor Maasoumi elaborates on how his research interests have evolved over time, highlighting his integration of economic theory with econometric methodology to better address real-world challenges. Professor Maasoumi also discusses his transition from the UK to the US, his collaborations with leading economists such as Clive Granger and Jeff Racine, and his long-standing role as Editor of Econometric Reviews . The interview concludes with his views on the evolution of econometrics, the current challenges in the field, and his advice for young researchers. This discussion aims to provide readers with deeper insight into key econometric concepts such as model misspecification, nonlinear testing, and multidimensional measures of inequality and welfare – and how these issues shape our understanding of the real economy.
Open Access
Quantifying Extreme Risks in High-Frequency Financial, Energy, and Commodity Markets

July 10, 2025

Vitali Alexeev, Katja Ignatieva

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This paper develops a robust framework for tail risk assessment in financial, energy, and commodity markets leveraging Tail Conditional Expectation (TCE) within the versatile family of skewed Generalised Hyperbolic (GH) distributions. The GH distributions effectively capture the asymmetric, heavy-tailed behaviour of high-frequency market data, which, in combination with TCE, addresses the limitations of traditional risk measures like Value-at-Risk (VaR). Focusing on exchange-traded funds (ETFs) – USO (crude oil), GLD (gold), and SPY (S & P 500) – we extend the TCE measure to multivariate portfolios and decompose portfolio-level risk into individual asset contributions. This provides clear insights into each asset’s role in overall tail risk. To capture evolving market dynamics, we implement a rolling-window analysis for time-varying TCEs, validated through rigorous backtesting. The results demonstrate the model’s conservative and reliable performance in extreme risk prediction. By offering a flexible and accurate approach to quantify tail risks, our study empowers market participants to manage volatility, navigate systemic shocks, and design effective risk mitigation strategies across diverse financial environments.
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Uncertainty Unpacked: State-Level Housing Market Dynamics in the Face of Shocks

July 8, 2025

MeiChi Huang

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This study examines the impacts of three varieties of uncertainties on the US state-level housing markets using the Stochastic Volatility in Mean Vector Autoregression (SVMVAR) framework. The findings reveal that all forms of uncertainty intensify in the COVID-19 period. Across most states, shocks to housing volume and price uncertainty generally influence housing volumes and prices in the same direction, although the magnitude of responses to housing price uncertainty differs significantly between housing prices and volumes. The uncertainty spillover is unidirectional: an increase in housing price uncertainty reduces fundamental uncertainty but amplifies volume uncertainty, but the reverse is not observed. The findings highlight the influential roles of housing price uncertainty in driving the real economy and housing markets at state levels.
Open Access
Two-Step Optimal Prediction Under Phillips Triangular Cointegrated System

June 26, 2025

Yun-Yeong Kim

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This study proposes a two-step optimal best linear predictor (OBLP) under Phillips triangular cointegrated system, deduced from a two-step optimal forecasting method, for non-stationary level variables cointegrated with fundamental variables. In the first step, a cointegration equilibrium is estimated. The difference between the cointegration equilibrium and the other predicted variables is optimally forecasted in the second step, with conditional expectations estimated by the lagged fundamental differences and cointegration errors and summed with the cointegration equilibrium. We show that the OBLP has the lowest mean squared forecasting error among linear forecasting methods, such as random walk, cointegration, and augmented error correction models. In the second step, the cointegration error correction model is converted into a vector autoregression model consisting of the cointegration error and the fundamental differences of the variables and is used to estimate conditional expectations. Simulation results comparing the other predictors with the OBLP and forecast results for the US GDP and consumption applying the OBLP support the theoretical predictions of the forecasting efficiency of the OBLP.
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A Multivariate Nonlinear Analysis of China’s GDP and World Oil Price and Its Implications

June 26, 2025

Fredj Jawadi, Ruey S. Tsay

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This paper reviews the relationship between China’s GDP and world oil price in recent decades to investigate whether the growth and evolution of the Chinese economy have a significant impact on the global oil market and to measure to what extent oil shocks affect China’s economy. To this end, we propose a multivariate threshold autoregressive model for the two time series and study the associated nonlinear impulse response functions. We also contrast the implications of the nonlinear model with those of the linear model and other alternative specifications. Our findings show certain strong nonlinear effects between China’s GDP and the oil sector. In particular, our nonlinear VAR model points to the presence of nonlinear causality effects when oil price declines, suggesting further evidence of asymmetrical interactions. Our results help to clarify previous studies on the effects of lead-lag between oil price and the real economy as a whole and China in particular. Our findings appear to be in line with Hamilton’s (1983. “Oil and the Macroeconomy Since World War II.” Journal of Political Economy 91 (2): 228–48) work, which points to significant nonlinearity in this relationship. In addition, our On/Off Threshold VAR model allows us to reproduce the time-varying relationship between oil price and China’s GDP.
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Panel Smooth Transition Model with Covariate-Dependent Thresholds and its Application to the Nexus between Investment and Cash Flow

June 18, 2025

Lixiong Yang, Yanli Xie, Liangyan Yao

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This paper introduces a panel smooth transition model with a covariate-dependent threshold (PSTCT). To overcome the difficulty in estimating threshold parameters of covariate-dependent thresholds, we develop a new algorithm based on the within-group transformation and simulated annealing (SA) technique. We also suggest test statistics for threshold effect, threshold constancy and cross-section dependency in the proposed model. A variable selection procedure is suggested to choose the covariates that affect the threshold. An extension to the setting with multiple regimes is also discussed. Monte Carlo simulations are conducted to investigate the finite sample properties of the proposed estimation and testing procedures. The model is illustrated by revisiting the relationship between firms’ investment and cash flow using the dataset of González, A., T. Teräsvirta, D. van Dijk, and Y. Yang. 2017. “Panel Smooth Transition Regression Models.” CREATES Research Paper . Comparing the proposed model with PSTR model of González, A., T. Teräsvirta, D. van Dijk, and Y. Yang. 2017. “Panel Smooth Transition Regression Models.” CREATES Research Paper , we find different empirical results after incorporating the covariate-dependent thresholds setting, highlighting the importance of splitting the sample based on a number of indicator variables in the cash flow/investment relationship.
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Does Gender Parity in Higher Education Respond Asymmetrically to Remittances? Evidence from Morocco

June 12, 2025

Oussama Zennati, Jamal Bouoiyour

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This study examines the dynamic relationship between migrant remittances and gender parity in higher education in Morocco from 1975 to 2023. While existing studies primarily focus on the gendered impact of remittances on primary and secondary education in home countries, the effects on tertiary education remain largely unexplored. Furthermore, these studies often assume a symmetrical impact of remittances, which may not be the case. Using linear ARDL modelling, we demonstrate that remittances have a positive and long-term impact on gender parity in higher education in Morocco. This finding underscores the role of remittances in reducing gender inequality in higher education in Morocco. To explore potential asymmetries, we employed a nonlinear ARDL model, which revealed a short-run asymmetrical impact of remittances on parity in higher education. Our findings are robust to alternative variables and demonstrate the potential of remittances to enhance human development indicators in Morocco. Additionally, remittances serve as an effective tool for achieving sustainable development goals in Morocco.
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Frequency Connectedness and Portfolio Implication Between Financial, Green and Commodity Markets: A TVP-VAR Approach

June 9, 2025

Nawel Ben Amor, Amal Ghorbel, Slah Bahloul

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This paper examines the dynamic connectedness and optimal hedging strategy of the global stock markets indices, commodities and green bonds. We use the novel frequency TVP-VAR method, and then we apply different portfolio construction approaches, namely MVP, MCP and MCoP, and bivariate hedge ratio. We find that stock markets are more interconnected during coronavirus pandemic and Russo-Ukraine conflict. Furthermore, empirical results suggest that the connectivity between variables depends on short-term shock transmissions. Gold act always as the largest shock receiver during periods of crisis. While Platinum and Silver are the main nets-transmitters. Our results indicate that the dynamic portfolio weights for MCP and MCoP appear to be comparable, but notably distinct from the MVP approach. In general, our findings indicate that the majority of commodities offer substantial diversification advantages compared to various stock markets, particularly during crisis periods, surpassing the benefits provided by green bonds. Most of them provide hedging benefits, particularly in comparison to the global index of developed countries and especially during stressful period.
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Another Look into Tail Risk Connectedness Using Network Modelling: Evidence from European Stock Markets

May 28, 2025

Raffaele Mattera, Javier Sanchez-Garcia

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This paper proposes an approach for measuring tail risk connectedness in financial networks by leveraging spatial methods, particularly the spatial autoregressive model, applied to Value-at-Risk (VaR) and Expected Shortfall (ES) estimates. Given the definition of the network structure, and departing from traditional methods reliant on volatility spillovers, our approach aims to capture the effect of the nature of the event on the tail dimension of market interconnectedness, offering insights beyond conventional metrics. Our results show that since the nature of the event substantially affects the convergence (divergence) of the response of the agents of the financial network to a shock, accounting for this effect is crucial to correctly measure its transmission. Since not all shocks are similar, events such as the Great Recession or the COVID-19 pandemic do not affect the tail risk of the financial network in a similar way, even when volatility spillovers increase in both cases. The relevance of considering the source of the shock is shown through an empirical analysis of the most important European stock markets, demonstrating the efficacy of the proposed approach in assessing systemic risks, therefore providing a valuable tool for policymakers, investors, and financial regulators.
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Estimation of High-Dimensional Matrix Factor Models with Change Points

May 23, 2025

Lijie Peng, Guchu Zou, Jianhong Wu

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In this paper, we focus on the high-dimensional matrix factor models with change points. We first consider the matrix factor model with a single change point, and propose a least squares estimation method to identify the change point. When the number of change points is unknown, a two-step estimation procedure is developed to identify all the change points. Under some mild conditions, the estimator of the number of change points can be proved to be consistent, and the distance between the estimated and true change points can be proved to be stochastically bounded. Monte Carlo simulation study and real data analysis are carried out for illustration.
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Identifying Shock Propagation Mechanisms in Global Equity Markets

May 22, 2025

Vance L. Martin, Saikat Sarkar

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The intertemporal capital asset pricing model with time-varying price and quantity risk factors, is used to study the propagation mechanisms linking expected risk premia with shocks in global equity markets. The model allows for linear and nonlinear propagation channels with the relationship between expected risk premia and world and country shocks characterized by a bivariate cubic. Using daily data on developed and emerging country equity returns, the empirical results show that country risk prices are exposed to world risks, although the signs differ between developed and emerging countries. Country risk factors are especially important for risk prices in Asia-Pacific countries as well as selected emerging countries. Of the financial risk factors investigated, volatility risk is important for all developed countries, and currency basis risk is important for all emerging countries. The nonlinear propagation mechanisms linking shocks and expected risk premia are economically significant and show that the size and sign of shocks are important. Implications of the empirical results for international portfolio diversification are also investigated using a range of simulation experiments.
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Environmental Tax and Macroeconomic Dynamics under Vertical Production Structure

May 22, 2025

Pengqing Zhang, Jiancai Pi

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Both upstream and downstream sectors can generate pollution, but such a vertical production structure has seldom been studied. This paper embeds upstream and downstream linkages into the environmental dynamic general equilibrium model, and explores both aggregate and sectoral effects of the environmental tax on macroeconomic dynamics. We find that: (i) the environmental tax designed for a 20 % reduction in emissions in the economy with upstream and downstream linkages is lower than that without the linkages; (ii) taxing only the upstream sector is more efficient for a moderate environmental tax rate than taxing both sectors, but to achieve a 20 % reduction goal, it will double abatement costs and reduce social welfare; (iii) there is an inverted U-shape implication of the environmental tax on output with respect to the degree of upstream and downstream linkages.
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Inflation: Demand Pull or Cost Push? A Markov Switching Approach

April 16, 2025

Pu Chen, Willi Semmler

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In this paper, we develop a Markov switching method to quantify the relative contributions of cost-push and demand-pull to current inflationary pressures. This approach aids in studying whether the inflation is short-lived or more persistent. We apply this method to Australian data and identify three episodes in the last 25 years when the inflation rate exceeded 4 %. All three episodes were primarily driven by cost-push factors. Our results reveal that monetary policy is more effective in controlling demand-pull inflation but less so in controlling cost-push inflation. This observation explains why the episodes of relatively higher inflation were predominantly driven by cost-push factors. Furthermore, we contrast our findings with US inflation drivers.
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Macroeconomic Imbalances and Financial Stress Among BRICS: Analysis of Frequency-Dependent and Asymmetric Causal Nexuses

April 16, 2025

Mohammed Armah, Ebenezer Bugri Anarfo, Emmanuel Numapau Gyamfi, Godfred Amewu

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This study investigates the intricate and evolving causal relationship between macroeconomic imbalances and financial stress in BRICS nations. To analyse these dynamics across different time scales, thus enabling timely and policy intervention, we employ an asymmetric, noise-reducing-domain ICEEMDAN-based non-parametric model supplemented by a time-varying vector autoregressive model spanning from 1998 to 2021. Our findings reveal that financial stress and macroeconomic imbalance in BRICS exhibit both frequency-dependent and asymmetric linkages, shedding light on the mechanisms underlying financial contagion and market instability in BRICS nations. Specifically deteriorating financial conditions are linked to heightened macroeconomic instability, whereas periods of low stress correspond to improved macroeconomic condition. The results underscore the need to strengthen the macroeconomic frameworks with inflation serving as a critical nominal anchor and focal point of overarching policy guidelines. Proactive monitoring and responses to accumulation of financial imbalances are essential. The study recommends that policymakers should implement fiscal and monetary measures that prioritize sustainable economic growth while reducing reliance on debt and maintaining current account balance to mitigate financial vulnerabilities.
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A Test for Time-Varying Smooth Transition Conditional Covariance Models in Multivariate Time Series

April 15, 2025

Bilel Sanhaji

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This paper introduces a novel test designed to assess the validity of time-varying smooth transition conditional covariance models. We develop a model driven by five scalar parameters in order to build the Lagrange Multiplier test within the framework of multivariate conditional heteroskedastic time series models with smooth transition functions. We detail the development of these tests, emphasizing their applicability. The methodology is scrutinized through Monte Carlo simulations, providing insights into its finite sample properties. Additionally, empirical illustrations underscore the practical relevance of the proposed tests, demonstrating their efficiency in capturing time-varying smooth transitions within financial datasets.
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A Time-Based Pricing Game Considering Echelon Utilization in the Battery Leasing Market

March 26, 2025

Junhai Ma, Xue Ding, Li Zhao, Xiaoyan Wang

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At present, many electric vehicle (EV) companies consider the adoption of a battery leasing model as part of their sales strategy, addressing the issue of higher prices for energy vehicles (EVs) compared to internal combustion engine vehicles (ICEVs) of the same level. In order to enhance the development of the battery leasing model in the EV market, this research explores pricing strategies within the battery supply chain operating under the “battery leasing + echelon utilization” model. Both a Stackelberg and a dynamic system model are proposed with the consideration of echelon utilization. We investigate how the echelon utilization rate, battery quality, and recycling price influence pricing decisions for both battery manufacturers and EV companies. These insights offer guidance for these entities in formulating appropriate pricing strategies. Introducing a long-term repeated game model, we analyze system stability and chaos conditions, the finding from the dynamic model discloses how different behaviors impact the long-term profitability of all parties involved. Furthermore, we propose a chaos control method. Our findings provide valuable managerial insights for battery manufacturers and EV companies.
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Ripple Effects of the US-China Tension on Asian Emerging and Frontier Markets with Portfolio Implications

March 24, 2025

Naveed Khan, Ozair Siddiqui, OlaOluwa S. Yaya, Xuan Vinh Vo

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In this paper, we investigate the ripple effects of the US-China tension on Asian emerging markets (India, Indonesia, South Korea, Malaysia, Philippines, Taiwan, and Thailand) and Asian frontier markets (Bangladesh, Sri Lanka, Pakistan, Bahrain, Kuwait, Vietnam, and Oman) for the period spanning from February 2013 to February 2024. The US-China Tension Index (UCTI) is a proxy variable for the US-China tension. Time-varying parameter vector autoregression, wavelet coherence, and hedging effectiveness techniques are employed for the empirical analysis. Findings show that the total connectedness between UCTI and Asian frontier markets is stronger than that of Asian emerging markets. Moreover, findings reveal that, in the case of Asian emerging markets, Indonesia, South Korea, Malaysia, Philippines, Taiwan, and Thailand are net transmitters of return spillovers, while India is a net receiver. In the case of Asian frontier markets, we find that Sri Lanka, Bahrain, Pakistan, Kuwait, and Oman are net transmitters. At the same time, Bangladesh and Vietnam are net receivers of return spillovers. In the frequency co-movement analysis, we report a positive correlation between UCTI and these markets at lower frequencies. In comparison, we report a negative correlation at the middle and higher frequencies. Furthermore, we report that hedging ratios highlight the significance of modifying portfolio weights in uncertain times when looking for investment opportunities in Asian emerging and frontier markets. Similarly, our findings highlight important implications for investors and portfolio managers to optimize their investments with risk-adjusted portfolios.
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Quasi-Maximum Likelihood for Estimating Structural Models

March 19, 2025

Malek Ben-Abdellatif, Hatem Ben-Ameur, Rim Chérif, Tarek Fakhfakh

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The estimation of the structural model poses a major challenge because its underlying asset (the firm asset value) is not directly observable. We consider an extended structural model that accommodates alternative underlying Markov processes, arbitrary debt payment schedules, several seniority classes, multiple intangible assets, and various intangible corporate securities. We derive the likelihood function given the observed time series of the firm equity values. Then, we use dynamic programming to solve the model and, simultaneously, extract the associated time series of the firm asset values (the pseudo-observations). Finally, the likelihood function is approximated and optimized, which results in the quasi-maximum likelihood (QML) estimates of the model’s unknown parameters. QML is highly flexible and effective. To assess our construction, we perform an empirical investigation, highlight the credit-spread puzzle, and discuss a partial remedy via jumps and bankruptcy costs.
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Fama–French Five-Factor Modeling: New Evidence from a Nonparametric Method

March 11, 2025

Zihao Hou, Viktor Manahov, Dimitrios Stafylas

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This study constructs a Fama–French five-factor model that considers the time-varying properties of the parameters and introduces a nonparametric method that estimates the factor loadings. We approach the topic from a micro perspective using high-frequency data to construct factors and models to evaluate the sensitivity of each factor on abnormal returns. The results show that the conditional alphas of portfolios are optimised, and the nonparametric model outperforms the traditional models. Our findings lead investors to consider the impact of parameter time variation when using multi-factor stock selection models to construct asset portfolios.
Open Access
Introducing sspaneltvp: A Code to Estimating State-Space Time-Varying Parameter Models in Panels. An Application to Okun’s Law

March 3, 2025

Mariam Camarero, Juan Sapena, Cecilio Tamarit

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This paper introduces a new code that provides researchers with a complete toolbox for estimating state-space time-varying parameter models. Our proposal extends the simple seminal framework into a panel-data one, combining both fixed (either common or country-specific) and varying components. Under specific conditions, this setting becomes a mean-reverting model, where the fixed mean parameter may include a deterministic trend. Regarding the transition equation, we allow for estimating different autoregressive alternatives and control instruments whose coefficients can be set up either common or idiosyncratic (this is particularly interesting for detecting asymmetries among individuals, i.e., countries, to common shocks). Furthermore, the GAUSS code allows for restrictions to the variances of both the transition and measurement equations. Finally, we illustrate our proposal with an empirical application to explore Okun’s Law for a panel of EU peripheral countries during the period 1965–2021.
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Monetary Policy and Growth at Risk: The Role of Financial Conditions

February 11, 2025

Licheng Zhang

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Previous studies mainly examine the monetary policy transmission to average growth outcomes, this paper instead studies the effects of monetary policy on the tail outcomes of GDP growth – Growth at Risk (GaR). We first use quantile regression to estimate the conditional distribution of GDP growth, and then estimate the impulse responses with smooth local projections. Our results show that GaR deteriorates in response to contractionary monetary policy shocks, suggesting an increase in macroeconomic tail risk. We investigate the role of financial conditions in the transmission of monetary policy to GaR. We find that contractionary monetary policy shocks lead to tighter financial conditions, and tighter financial conditions have significant negative effects on GaR. Moreover, we show that tighter financial conditions increase future recession risk in both the short and medium term.
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Factor Modeling for High-Dimensional Interval-Valued Data

February 4, 2025

Yan Guo, Guchu Zou, Jianhong Wu

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The paper considers an approximate factor model for interval-valued panel data with both large numbers of cross-section units and time series observations. A ratio-type estimator is proposed for the number of interval-valued factors in the approximate factor model. A variant of the estimator is also suggested, which is robust to the case with dominant factors. Under certain conditions, the estimators can be proved to be consistent. Moreover, the estimators of interval-valued factors and the pooled loadings can be obtained by the principal component analysis method for point-valued data. Monte Carlo simulation studies show that the proposed estimators have the desired finite sample properties.
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Realized Probability Index is a Better Market Timing Indicator

January 20, 2025

Haibin Xie, Boyao Wu, Yuying Sun, Shouyang Wang

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In practice, market timing is a well-known trading strategy among investors, and different indicators have been proposed for market timing methods. This paper compares three indicators used in market timing strategy: the return, the 0–1 binary index, and the realized probability index. It is shown that realized probability index is more informative and more efficient than the 0–1 binary index in terms of market timing, and tends to be more predictable than the return itself. This finding is interesting and important as it proves for the first time that the realized probability index is a more efficient market timing indicator and thus should be given more attention by both academic researchers and practitioners. An empirical study is performed on different stock indices, and the results confirm our finding.
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A Nonparametric Model for High-Frequency Energy Prices

December 24, 2024

Nikolay Gudkov, Katja Ignatieva

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This paper proposes an efficient approach for modelling a high frequency continuous time diffusion process for the dynamics of crude oil. While various applications of continuous time models are considered in the literature, the results on choosing the right model are mixed. We employ a very general non-parametric approach to capture the dynamics of the crude oil market proxied by United States Oil (USO) exchange traded fund. This approach is purely data driven and does not require specification of the drift or the diffusion coefficient function. The proposed nonparametric kernel-based estimation procedure relies on the local polynomial kernel regression, where the choice of a bandwidth parameter plays a significant role. We demonstrate that besides offering a convenient way of estimating the continuous-time models for energy prices, our estimation procedure performs well when dealing with predicting USO prices out-of-sample. The analysis is extended by incorporating possible jump diffusion, where the assumption of continuity of the stochastic process is relaxed and a jump component is added to the diffusion process. In addition, we extend our model by adding possible seasonalities in the underlying dynamics, which requires decomposing the price by means of the Maximum Overlap Discrete Wavelet Transform (MODWT) algorithm and applying nonparametric kernel-based estimation procedure to modelling of the deseasonalized prices.
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Dynamic Panel Threshold Spatial Durbin Model with an Application to the Relationship between Financial Development and Green Growth

December 16, 2024

Lili Wei, Chunli Zhang

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This paper studies computation, estimation, inference and specification testing in dynamic panel threshold spatial Durbin (DPTSD) model with multiple thresholds. We first develop a new Markov chain Monte Carlo (MCMC) based algorithm to jointly estimate the threshold parameters and simultaneously construct the confidence intervals for the parameters, after suggesting a within-group spatial two-stage least squares estimator. We then construct test statistics for threshold effect and the number of thresholds. Monte Carlo experiments indicate that the proposed estimator and tests have desired performance in finite samples. We finally apply the DPTSD model to investigate the relationship between financial development and green growth, and find that the empirical results based on the DPTSD model are quite different from these based on the dynamic panel threshold model.
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Monetary Policy Uncertainty in the United States and Investment Sentiment in Advanced Economies

November 26, 2024

Nahiyan Faisal Azad, Apostolos Serletis

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How does uncertainty originating from the future path taken by monetary policy enacted by the Federal Reserve in the United States affect the business confidence in other advanced economies? Does US monetary policy uncertainty affect economic activity in the United States and in Canada, France, Germany, Italy, Japan, and the United Kingdom. Motivated to answer these questions, we use monthly data and a bivariate GARCH-in-Mean VAR model. We also use a multivariate structural VAR model and a different measure of US monetary policy uncertainty, achieving identification by a combination of short-run and long-run restrictions. Our evidence shows that US monetary policy uncertainty, irrespective of how it is measured, has negative effects on the business confidence and output in the advanced G7 economies.
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To Bag is to Prune

October 25, 2024

Philippe Goulet Coulombe

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It is notoriously difficult to build a bad Random Forest (RF). Concurrently, RF blatantly overfits in-sample without apparent consequences out-of-sample. Arguments like the bias-variance trade-off or double descent cannot rationalize this paradox. I propose a new explanation: bootstrap aggregation and model perturbation as implemented by RF automatically prune a latent “true” tree. More generally, I document that randomized ensembles of greedily optimized learners implicitly perform optimal early stopping out-of-sample . So, letting RF overfit the training data is a dominant tuning strategy against nature’s undisclosed choice of noise level. Additionally, novel ensembles of Boosting and MARS are also eligible. I empirically demonstrate the property, with simulated and real data, by reporting that these new completely overfitting ensembles perform similarly to their tuned counterparts – or better.
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Impact of Disaggregated External Debt on Economic Growth: Evidence from Asian Developing Economies

October 10, 2024

Muhammad Dawood, Zhao Rui Feng, Muhammad Ilyas

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This study investigate the impact of total and disaggregated external debt on economic growth, across 32 Asian developing economies (ADE) from 1995 to 2020. The study applied the generalized method of moments (GMM) and dynamic common correlated estimator (DCCE) with interaction terms of institutional quality and macroeconomic policy to address the non-linearity, across-country heterogeneity, cross-sectional dependence and endogneity. The empirical results indicate that total external debt and its types initially harm economic growth, except for commercial creditors’ debt, which has positive effects. Short-term, private, and multilateral debt show weaker negative associations compared to long-term, public, and bilateral debt. Incorporating interaction terms in non-linear models reveal a shift from negative to positive impacts, highlighting the importance of robust institutional quality and stable macroeconomic policy in mitigating adverse debt effects. Our findings underline the necessity of tailored policies accounting for specific impacts of different debt types on economic growth. Moreover, highlight the significance of institutional quality and macroeconomic policy standards to manage risks, optimize debt management practices, adjust fiscal policies, and foster sustainable economic growth. Future research should further investigate the broad impact of domestic debt in conjunction with external debt across different countries, time periods, and methodological approaches.
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Sectoral Dependence and Financial Contagion in the BRICS Grouping: An Application of the R-Vine Copulas

September 30, 2024

Lumengo Bonga-Bonga, Johannes J. Hendriks

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This paper presents a novel approach utilising R-Vine copulas and tail dependence structures to distinguish between contagion and interdependence amid equity market interrelation. The approach is applied in the case of BRICS equity markets. Moreover, rather than analysing the equity markets in aggregate, our approach focuses on sectoral levels within BRICS equity markets to examine the nature of interrelation among them. Based on the tail dependence of sectoral equity market volatilities, empirical findings indicate minimal contagion events across various sectors of the BRICS equity markets. These results are corroborated through portfolio optimisation, demonstrating that markets identified as sources of contagion receive lower weights in the portfolio. This paper offers valuable insights for policymakers, investors, and asset managers by shedding light on the interrelationships among different sectors of the BRICS equity markets and the potential investment strategies that can be formulated based on co-movement types between these markets.
Open Access
Asymptotic Properties of ReLU FFN Sieve Estimators

September 5, 2024

Frank J. Fabozzi, Hasan Fallahgoul, Vincentius Franstianto, Grégoire Loeper

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Recently, machine learning algorithms have increasing become popular tools for economic and financial forecasting. While there are several machine learning algorithms for doing so, a powerful and efficient algorithm for forecasting purposes is the multi-layer, multi-node neural network with rectified linear unit (ReLU) activation function – deep neural network (DNN). Studies have demonstrated the empirical applications of DNN but have devoted less research to investigate its statistical properties which is mainly due to its severe nonlinearity and heavy parametrization. By borrowing tools from a non-parametric regression framework, sieve estimator, we first show that there exists such a sieve estimator for a DNN. We next establish three asymptotic properties of the ReLU network: consistency, sieve-based convergence rate, and asymptotic normality, and then validate our theoretical results using Monte Carlo analysis.
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Heterogeneity, Jumps and Co-Movements in Transmission of Volatility Spillovers Among Cryptocurrencies

August 27, 2024

Konstantinos Gkillas, Maria Tantoula, Manolis Tzagarakis

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We analyze properties identified in the price volatility of Bitcoin and some of the leading cryptocurrencies namely Litecoin, Ripple, and Ethereum. We employ Heterogeneous Autoregressive models (HAR) in both a univariate and multivariate level of analysis. First, the significance of heterogeneity and jumps is examined, considering the ability of several univariate HAR models, to predict realized volatility of cryptocurrencies. Second, we examine the relevance of realized volatility jumps and covariances in the transmission of volatility spillovers among cryptocurrencies. We perform a comparative spillover analysis of the multivariate HAR models in two versions, considering variances only and covariances as well. Our results indicate that covariances and jumps inclusion lead to an increase in spillovers. The time-varying spillover analysis indicates higher dependency between Bitcoin and the other cryptocurrencies mostly at short frequencies.
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Heterogeneous Volatility Information Content for the Realized GARCH Modeling and Forecasting Volatility

August 19, 2024

Wen Xu, Pakorn Aschakulporn, Jin E. Zhang

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As the demand for accuracy in volatility modeling and forecasting increases, the literature tends to incorporate different volatility measures with heterogeneous information content to construct the hybrid volatility model. This study focuses on one of the popular hybrid volatility models: the Realized Generalized Autoregressive Heteroskedasticity (Realized GARCH) and embeds various volatility measures, including the CBOE VIX, VIX1D, Realized Volatility, and Daily Range to examine their heterogeneous impact on the conditional volatility estimation and forecasting. To evaluate the impact of the volatility measures, we first construct a volatility response function. This involves calculating the difference in one-step-ahead conditional volatility forecasts that incorporate information from both return and volatility measures against the forecasts based on return innovations only. Subsequently, the variance share is calculated to evaluate its role in explaining future variations in the Realized GARCH. Our results show that among these four volatility measures, VIX is the most informative volatility. Although VIX1D is overemphasized by the literature, its significance in volatility forecasting remains substantial, confirming that risk-neutral volatility measures are generally more informative than physical measures. Finally, we also find that incorporating multiple risk-neutral volatility measures does not improve forecasting performance compared to using a single measure due to overlapping information.
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Likelihood-Ratio-Based Confidence Intervals for Multiple Threshold Parameters

August 8, 2024

Luiggi Donayre

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This paper proposes the inversion of likelihood ratio tests for the construction of confidence intervals for multiple threshold parameters. Using Monte Carlo simulations, conservative likelihood-ratio-based confidence intervals are shown to exhibit empirical coverage rates at least as high as nominal levels for all threshold parameters, while still being informative in the sense of only including relatively few observations in each confidence interval. These findings are robust to the magnitude of the threshold effect, the sample size and the presence of serial correlation. Applications to existing models with multiple thresholds for U.S. real GDP growth and for the wage Phillips curve demonstrate how the proposed approach is empirically relevant to make inferences about the uncertainty of threshold estimates.
Open Access
Which Global Cycle? A Stochastic Factor Selection Approach for Global Macro-Financial Cycles

August 8, 2024

Tino Berger, Sebastian Hienzsch

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Instead of assuming a certain factor structure, we statistically test for the factor structure driving common global dynamics in macroeconomic and financial data by employing a stochastic factor selection approach. Using a sample of 16 developed countries from 1996Q1 to 2019Q4, we present strong empirical evidence of a global macro-financial cycle and an independent global financial cycle. Moreover, the global macro-financial cycle we estimate is essentially the global business cycle identified in the literature. It captures the common global macroeconomic dynamics and drives a significant share of the comovement in the financial sector. The remaining commonality in financial variables is driven by separate global financial cycles: the global credit cycle and the global capital flow cycle.
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Determination of the Number of Breaks in Heterogeneous Panel Data Models

August 8, 2024

Lu Wang, Shuke Hu

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This paper considers a heterogeneous panel data model with an unknown number of breaks. We propose a so-called two-stage procedure to determine the number of breaks and detect the location of break points. The consistency of the estimated number of breaks and the estimated break points are established under fairly general conditions. Monte Carlo simulations and two empirical applications are provided to demonstrate the finite sample performance of the proposed method.
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Non-Linear Impact of Income Inequality on Mental Health: Evidence from Low and Middle-Income Countries

July 19, 2024

Ankita Mishra, Abebe Hailemariam, Preety Srivastava, Greeni Maheshwari

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In this study, we examine the relationship between income inequality and mental health using a sample of low and middle-income countries over the period 1990–2019. Using a dynamic panel threshold model that allows for endogeneity in both the regressors and threshold variable, we find a non-linear relationship between income inequality and the prevalence of mental health disorders. Specifically, income inequality is associated with reduced prevalence of mental health disorders at low levels of income inequality but after it surpasses a threshold Gini coefficient (estimated between 39 and 49), it has an adverse effect on mental health. The impact is more pronounced in low income and lower middle-income countries. We also find evidence of heterogenous effects by age and gender. Our findings indicate the importance of modelling non-linearity in the income inequality-health relationship and highlight the importance of keeping income inequality within reasonable bounds.
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Score-Driven Location Plus Scale Models: Asymptotic Theory and An Application to Forecasting Dow Jones Volatility

June 10, 2024

Szabolcs Blazsek, Alvaro Escribano, Adrian Licht

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Divisia Monetary Aggregates for India

May 27, 2024

Anirban Sengupta, Apostolos Serletis, Libo Xu

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In this paper, we are motivated by the fast growing literature that investigates the performance of Divisia monetary aggregates. We construct Divisia monetary aggregates for India using monthly data form January 2001 to March 2020 and present a comprehensive comparison across the Indian Divisia monetary aggregates at four levels of monetary aggregation, M1, M2, M3, and M4. We do so in the context of three classes of empirical models. In particular, we compute correlations between the cyclical components of the Divisia monetary aggregates and the cyclical component of the industrial production index. We test for Granger causality running from the Divisia monetary aggregates to industrial production. We also test for time-varying Granger causality. We find that the levels of the Divisia monetary aggregates Granger cause economic activity in India during normal times, but the causal link broke during and in the aftermath of the extremely unusual circumstances of the Covid-19 crisis.

Journal Impact Factor	0.9	2024, Journal Citation Reports (Clarivate, 2025)
5-year Journal Impact Factor	0.8	2024, Journal Citation Reports (Clarivate, 2025)
Journal Citation Indicator	0.26	2024, Journal Citation Reports (Clarivate, 2025)
CiteScore	1.4	2024, Scopus (Elsevier B.V., 2025)
SCImago Journal Rank	0.319	2024, SJR (Scimago Lab, 2025; Data Source: Scopus)
Source Normalized Impact per Paper	0.503	2024, CWTS Journal Indicators (CWTS B.V., 2025; Data Source: Scopus)
Mathematical Citation Quotient	0.06

Studies in Nonlinear Dynamics & Econometrics

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